Final answer:
The area of the circle with a diameter of 3.8n cm is approximately 11.33656n² square centimeters.
Step-by-step explanation:
To find the area of a circle, we use the formula A = πr², where A is the area and r is the radius. In this case, the diameter is given as 3.8n cm, which means the radius is half of that, or 1.9n cm. To find the area, we substitute the value of the radius into the formula: A = π(1.9n)². This simplifies to A = π(3.61n²), or approximately A = 3.14159(3.61n²). So, the area of the circle is 11.33656n² square centimeters.